She moved through the fair

Does anybody know the meaning of the following phrases:
"she crossed the green"

She walked across the grassy ground.

"in the same intellectual plane"?

understands the same concepts

this post reminds me of that haunting air - 'as she moved/walked through the fair' - I seem to have quite a number of versions - in the hands of a good singer it can be a masterpiece.

'in the same intellectual plane' sounds rather Lloyd Cole, but anyway a plane is a two dimensional shape of zero thickness, so to be aligned 'on the same plane' means that there is an unusual connection between two people.